Definition 21.1.1. Let \(F\colon C \to D\) and \(G \colon D \to C\) be two functors. An adjunction between \(C\) and \(D\) consists of a natural isomorphism \[ \Hom _D(F(-),-) \cong \Hom _C(-,G(-)) \] of functors \(C\catop \times D \to \An \). We often write \(F \dashv G\) to indicate that such an isomorphism has been given.
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